Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-7x+y &= -3 \\ -3x-y &= -6\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-10x = -9$ Divide both sides by $-10$ and reduce as necessary. $x = \dfrac{9}{10}$ Substitute $\dfrac{9}{10}$ for $x$ in the top equation. $-7( \dfrac{9}{10})+y = -3$ $-\dfrac{63}{10}+y = -3$ $y = \dfrac{33}{10}$ $y = \dfrac{33}{10}$ The solution is $\enspace x = \dfrac{9}{10}, \enspace y = \dfrac{33}{10}$.